Article history: Received 6 November 2009 Received in revised form 3 April 2010 Accepted 26 June 2010 Available online 3 July 2010

This paper describes a hierarchical spectral method for the correspondence matching of point-sets. Conventional spectral methods for correspondence matching are notoriously susceptible to differences in the relational structure of the point-sets under consideration. In this paper we demonstrate how the method can be rendered robust to structural differences by adopting a hierarchical approach. ...

In a recent article [2] Dutt, Greengard and Rohklin define two newmethods of deferred correction. Convergence for the the first method, using one step methods, has been proven in Hansen [8]. In this paper we augment the theory presented in [8] and use this to prove convergence for the second deferred correction method in [2] using linear k-step methods. This method has been known as Spectral De...

3 Spectral Method 5 3.1 A Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Toy Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 General Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.4 Color agreement problems . . . . . . . . . . . . ....

Article history: Received 22 May 2013 Received in revised form 11 October 2013 Accepted 23 October 2013 Available online 31 October 2013

A deviation from the slow roll may shift the spectral index and its running. Such a deviation is very generic in inflationary models since the slow-roll equation is not the exact solution of the field equation. We calculate the spectral index and its running with non-vanishing deviation parameter, showing that the deviation parameter is a “hidden” parameter of the standard calculation. A runnin...

We review the connection between inflationary models and observations and concentrate to describe models based on softly broken supersymmetry, in particular running mass models, and their predictions. We then present a fit of the spectral index of the curvature perturbation, assuming a flat ΛCDM cosmology.

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as a set of non-overlapping cubic regions, plus a set of maps to identify the faces of adjoining regions. The differential structure on these manifolds is fixe...

In the past few years we have been involved in the development and implementation of parallel finite element and pseudo-spectral methods for porous media flow. In this paper we present a brief review of our methods and show several examples of highly nonlinear simulations in two and three-dimensions, on different current high performance computers. New issues on finite element techniques and ps...

An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational p...